The 'Gladiator' star is tipped to take on the role of the media mogul in a movie based on 'Good Times, Bad Times', the memoirs of former Sunday Times editor Sir Harold Evans.
A source told the Daily Star newspaper: ''You have to be brave to play someone like Murdoch. Russell can do it.''
Colin Firth is believed to be up for the role as Harold, but no deals are yet in place.
Leon Lecash, creative director of what's it all about?, which is making the movie said: ''The film will be a drama, either for the big screen or television. It is very early days as the option deal with Harry was only just completed.
''No actors or even writers have been signed up yet.''
The film will focus on then-Prime Minister Lady Margaret Thatcher's dealings with the Australian tycoon.
Evidence is said to suggest she manipulated rules to facilitate The Deal for Murdoch to buy The Times newspaper in 1981 in return for favourable publicity for her party.
Leon added to the Evening Standard newspaper: ''Murdoch went to Chequers to talk about the deal, which was never brought to the attention of the Monopolies Commission.
''Harry had suspicions that some intimate contacts were taking place between Murdoch and Thatcher, with late-night whisky drinking in Downing Street when Murdoch was let in by the back door. This type of stuff came to light recently when Sir Bernard Ingham's notes were released under the 30-year rule. Much of what Harry wrote about Murdoch when they fell out in 1983 is so prescient he has said he didn't know whether to laugh or cry.''